
where the last step follows by Jensen's inequality and the fact that
that \(A \mapsto \operatorname{Tr}((A + \lambda I_d/n)^{-1}A)\)  is a concave map for \(A \succeq 0\) .
Note that the quantity quantity \(\operatorname{Tr}((\Sigma + \lambda I_d/n)^{-1}\Sigma )\) , known as the effective dimension (cf. [1]}), is never larger than \(d\) .

